Artifact reduction decompression method and apparatus for interpolated images

ABSTRACT

A method to reduce the distortion introduced by lossy compression of interpolated images. The interpolation represents a constraint. If the output of the compression algorithm does not satisfy the constraint then the estimate of the output can be improved by re-imposing the constraint. An alternating projection algorithm is used to impose both the interpolation constraint, and the requirement that the image compress to the observed compressed output. This involves finding the orthogonal projection alternately on the space of interpolated images, and on the set of images that quantize to the appropriate image produced by the compression algorithm. Although this algorithm is not restricted to the correction of errors in block coding schemes, the explicit introduction of the interpolation constraint allows this algorithm to outperform all other iterative algorithms that attempt only to remove blocking artifacts introduced by transform coders. An important special case is the case of color interpolated images, and JPEG compression. This method is able to improve the output image both in terms of mean squared error and visual appearance.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to digital image processing and, moreparticularly, to decompressing interpolated images.

2. Description of the Related Art

In many image processing pipelines a compromise has to be made betweenthe number of bits used to store an image and the distortion introducedby compressing it. Although lossless compression schemes can achievesome saving of the storage required, for larger compression ratios it isusually necessary to use a lossy compression method. Many lossycompression schemes are known, JPEG (Joint Photographic Experts Group)is typical of such schemes. See, for example, the baseline version ofthe JPEG algorithm (ITU-T Rec.T.81/ISO/IEC 10918-1 "Digital Compressionand Coding of Digital Still Images").

Although lossy coders are typically designed so that the loss introducedis as imperceptible as possible, there will always be artifacts of thecompression and these become increasingly objectionable as thecompression ratio is increased. Sometimes it is possible to improve thecompressed image, for example by attempting to remove the blockingartifacts of JPEG (see, for example, R. Eschbach, Decompression ofStandard ADCT-compressed Images, U.S. Pat. No. 5,379,122, January 1995),but in general there is limited room for improvement of compressedimages.

Thus, it can be seen that lossy image compression techniques imposeimage fidelity limits upon image capture or display devices, and hinderthe use of these devices in many applications.

Therefore, there is an unresolved need for an image decompressiontechnique that can improve the fidelity of decompressed lossy-compressedinterpolated images by decreasing the error introduced for a givencompression ratio.

SUMMARY OF THE INVENTION

A process and apparatus is described to reduce the distortion introducedby lossy compression of interpolated images. The interpolationrepresents a constraint. If the output of the compression algorithm doesnot satisfy the constraint then the estimate of the output can beimproved by re-imposing the constraint. An alternating projectionalgorithm is used to impose both the interpolation constraint, and therequirement that the image compress to the observed compressed output.This involves finding the orthogonal projection alternately on the spaceof interpolated images, and on the set of images that quantize to theappropriate image produced by the compression algorithm.

Although this algorithm is not restricted to the correction of errors inblock coding schemes, the explicit introduction of the interpolationconstraint allows this algorithm to outperform all other iterativealgorithms that attempt only to remove blocking artifacts introduced bytransform coders.

An important special case is the case of color interpolated images, andJPEG compression. This method is able to improve the output image bothin terms of mean squared error and visual appearance.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be readily understood by the following detaileddescription in conjunction with the accompanying drawings, wherein likereference numerals designate like structural elements, and in which:

FIG. 1 is a block diagram illustrating an apparatus for processing adigital image using an interpolated image decompression scheme thatpractices image compression artifact reduction according to the presentinvention;

FIG. 2 is a diagram illustrating a raw data (R) mosaic suitable forapplying image compression artifact reduction according to the presentinvention;

FIG. 3 is a diagram illustrating a first interpolated data (I₀) mosaicsuitable for applying image compression artifact reduction according tothe present invention;

FIG. 4 is a diagram illustrating a second interpolated data (I₁) mosaicsuitable for applying image compression artifact reduction according tothe present invention;

FIG. 5 is a flow chart illustrating an interpolated image decompressionprocess that practices image compression artifact reduction according toone embodiment of the present invention;

FIG. 6 is a block diagram illustrating an interpolated imagedecompression apparatus that practices image compression artifactreduction according to one embodiment of the present invention;

FIG. 7A is a representative comparison of Root Mean Squared Error of thegreen channel of a bilinear interpolated image as a function ofcompression ratio between a decompression scheme according to oneembodiment of the present invention and a traditional imagedecompression scheme;

FIG. 7B is a representative comparison of Root Mean Squared Error of thered channel of a bilinear interpolated image as a function ofcompression ratio between a decompression scheme according to oneembodiment of the present invention and a traditional imagedecompression scheme;

FIG. 7C is a representative comparison of Root Mean Squared Error of theblue channel of a bilinear interpolated image as a function ofcompression ratio between a decompression scheme according to oneembodiment of the present invention and a traditional imagedecompression scheme; and

FIG. 8 is a diagram illustrating a system for orthogonal projection ontothe space of interpolated signals according to one embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention are discussed below with reference to FIGS.1-8. Those skilled in the art will readily appreciate that the detaileddescription given herein with respect to these figures is forexplanatory purposes, however, because the invention extends beyondthese limited embodiments.

FIG. 1 is a block diagram illustrating an apparatus 100 for processing adigital image using an interpolated image decompression scheme thatpractices image compression artifact reduction according to the presentinvention. In FIG. 1, a raw digital color image 120 is acquired 110. Rawimage 120 undergoes interpolation and color space transformation 130before being compressed 140, which yields compressed image 150. Finalimage 170 is decompressed 160 from compressed image 150 so that finalimage 170 can be output 180.

Although the following discussion will be made within the context of adigital camera and color interpolation, the image compression artifactreduction scheme can be practiced on any interpolated digital image. Forexample, where a color or grayscale image is interpolated to alter itssize. Also for example, for alternate embodiments, image acquisition 110can be performed by a facsimile or scanning apparatus. Similarly, outputof final image 170 can be performed by any known image output device,(e.g., a printer or display device). Furthermore, although the followingdiscussion will use a 24-bit digital color image as an example, it is tobe understood that images having pixels with other color resolution maybe used. Moreover, although the JPEG algorithm will be used in theexample, it is to be understood that the image compression artifactreduction scheme can be practiced on any similar lossy compression.

To get the maximum benefit from the JPEG algorithm, it is usual totransform to a luminance/chrominance space such as YUV or YCrCb. Tocarry out this transformation it is first necessary to demosaic theimage to have a full 24-bit image. There are a variety of algorithmsthat carry out this color interpolation.

The Color Interpolation Block

The raw data of digital color image 110 typically consists of a mosaicof data samples from the three color planes. Before using an algorithmsuch as JPEG, we must interpolate to a 24-bit image. In other words, tothe raw data image R shown in FIG. 2, we must add the two images I₀ andI₁ shown in FIGS. 3 and 4, respectively, to make the full color image.Obviously these last two images are calculated from the raw data R andcontain no new information. We will refer to the full 24-bit image interms of three planes, i.e. we shall denote the image (R, I₀, I₁).

Thus, FIG. 2 is a diagram illustrating a raw data (R) mosaic suitablefor applying mosaiced image compression artifact reduction according tothe present invention. FIGS. 3 and 4 are corresponding diagrams thatrespectively illustrate first and second interpolated data (I₀ and I₁)mosaics suitable for applying mosaiced image compression artifactreduction according to the present invention. In FIG. 2, red sensors(201, 203, 221, 223), green sensors (200, 202, 211, 213, 220, 222, 231,233) and blue sensors (210, 212, 230, 232) are arranged in afour-by-four mosaic. The color mosaic of FIG. 2 is an example only.Various other mosaic patterns are possible.

The values measured by the sensor of the mosaic are then interpolated toprovide the missing values. For example, according to a bilinearinterpolation scheme, a red value for the location of green sensor 211can be formed by averaging the red values measured by red sensors 201and 221. This is shown as interpolated red value 311 of FIG. 3.Similarly, a blue value for the location of green sensor 211 can beformed by averaging the blue values measured by blue sensors 210 and212. This is shown as interpolated blue value 411 of FIG. 4.

Therefore, in FIG. 3, red values (300, 302, 311, 313, 320, 322, 331,333), green values (310, 312, 330, 332) and blue values (301, 303, 321,322) are arranged in an interpolated four-by-four mosaic whichcorresponds to the four-by-four sensor mosaic of FIG. 2. Similarly, inFIG. 4, red values (410, 412, 430, 432), green values (401, 403, 421,422) and blue values (400, 402, 411, 413, 420, 422, 431, 433) arearranged in an interpolated four-by-four mosaic which corresponds to thefour-by-four sensor mosaic of FIG. 2.

Having been demosaiced, the 24-bit image is color transformed and JPEGcompressed, which of course involves some loss. The loss is typicallyspread throughout all of the colors at all of the locations andintroduces undesirable artifacts into the decompressed image. However,as will be described below in greater detail, the decompressiontechnique of apparatus 100 has been modified to use an interpolatedimage decompression scheme that practices image compression artifactreduction according to the present invention.

Image compression artifact reduction according to the present inventionoperates by exploiting the fact that sometimes one has some a prioriinformation about the image. For example, that the image possesses someproperty which is easily identifiable.

Consider the simple case where an image has been scaled by a factor offour using pixel replication. In this case we know that 4×4 blocks ofpixels have identical values in the original image. After the image goesthrough a lossy compression algorithm however, pixels in those 4×4blocks will no longer have identical values, because the quantizationnoise added by the compression affects individual pixels differently(although they will probably be numerically close).

We know that the original came from the set of images that was pixelreplicated by four so we can improve our estimate of the decompressedimage if we restrict our attention only to those images that have thisproperty. We could in fact improve our estimate of the original value ina given 4×4 block by replacing the current values by the average overthe whole block. Thus, instead of taking the compressed image, we selectfrom among the set of images that are pixel replicated by four, the onethat is closest to the compressed original. Although simplified fordidactic purposes, this is the basis of the post-processing algorithmthat we apply.

Post-processing Algorithm

In general when considering a compressed image, we know only one thingabout the original from which it is derived, namely that the originalcompresses to the image output by the compression algorithm. However, ifthe image has been interpolated by some known algorithm, we then knowtwo things about the original image. First, we know that the image hasbeen interpolated in the prescribed way. Secondly, we know that theimage compresses to the image output by the compression algorithm

The decompressed image satisfies the second of these properties, but notthe first. If we could find an image that had both properties then thisimage would satisfy all of the properties that we know the originalimage to possess.

An algorithm to find an image that satisfies two constraints is thealgorithm of Projection On Convex Sets (POCS). Provided that each of theconstraints corresponds to a convex set in the image space, we can findan image that satisfies both by alternately taking the orthogonalprojection on the two sets. Taking the orthogonal projection merelymeans finding the closest image (using some appropriate measure ofdistance) with the desired constraint. The algorithm thus can bewritten:

0. Start with an estimate of the decompressed image.

1. Find the closest image that has been interpolated in the prescribedway.

2. Find the closest image that compresses to the same compressed outputas the original.

3. GOTO 1 unless convergence.

This algorithm is known to converge to an image that satisfies bothconstraints. Although perfect convergence occurs only after an infinitenumber of iterations, in practice excellent results are often achievedafter a finite and small number of iterations. Even a single iterationoften improves the solution considerably.

Recall that the algorithm works provided the constraint sets are convex,and we can implement orthogonal projections onto them. Fortunately theset of images that have been interpolated by a linear algorithm such asbilinear interpolation corresponds to a space, which is always convex.The set of images that compress to a given compressed image alsocorresponds to a convex set. Usually, the image is transformed usingsome linear transformation, and the transform coefficients are quantizedusing scalar quantizers. The set of images that compress to the sameoutput using such a system is always convex provided that the lineartransformation is unitary.

Performing the orthogonal projections onto these two sets can be complexdepending on the exact nature of the interpolation and compressionscheme used. However, for most interpolation schemes the appropriateprojection can be carried out using two filtering operations.

Projection onto Space of Interpolated Signals

As mentioned, carrying out the orthogonal projection onto the space ofinterpolated images is easily performed. We explain the one dimensionalcase for simplicity. A one dimensional interpolated signal can beexpressed as ##EQU1## where M is the interpolation factor, and h(·) isthe interpolating filter kernel. The orthogonal projection onto thespace of such signals can be implemented using the system 800 set forthin FIG. 8. In this figure, ##EQU2## where G*(e^(j)ω) is the timereversed version of filter G(e^(j)ω) and √· denotes spectralfactorization.

We note that the filter G(z) in general has an infinite impulseresponse.

In the figure the signal first passes through a filter G(z) 810 and thenthe combination of a downsampler 820 and upsampler 830, the combinedeffect of which is to retain only every M-th sample of the filteredsignal. Finally the resultant signal passes through the filter G*(z)840. Because we use two filtering and a sampling rate change, our methodis clearly distinct from Eschbach.

Similar relations hold for carrying out the orthogonal projection ontomultidimensional interpolated space, although in two and higherdimensionals spectral factorization are difficult to implement.

There are many different ways of implementing a projection onto aninterpolated space, for example Fourier Transform.

We point out that even though orthogonal projections are the mostdesirable, using a non-orthogonal projection works well in practice formost cases. This is important when the orthogonal projection isdifficult to implement. In practice using a non-orthogonal projectionmeans that instead of taking the closest image that satisfies thedesired property, we take one that is not necessarily closest, but stillsatisfies the desired property.

We point out that for one embodiment of the invention, the projectiononto the interpolated space takes place in RGB space, while theprojection onto the set of images that produce the encoded stream isgenerally in YUV. Although different measures of closeness are used inthese two spaces, the algorithm converges well.

We also point out that if additional constraints on the image are knownor desired, they can be included as a third step in the iterative loopof the algorithm. For example, a smoothness constraint could be imposedby lowpass filtering.

The projection onto the set of images that compress to the same outputcan be performed using a variation of the compression scheme where thequantization values are altered. This is covered in detail in R.Eschbach, Decompression of Standard ADCT-compressed Images, U.S. Pat.No. 5,379,122, January 1995. Thus both projections can be performedsimply, and we can implement the algorithm with reasonable complexity.

Color Interpolation of Digital Camera Images and JPEG Compression

Although the algorithm we have outlined works for any interpolationscheme whose range is a space, and any convex lossy compressionalgorithm, a particularly important case is that of color interpolationof mosaiced digital camera images, and JPEG compression.

The Compression Block: JPEG

JPEG is a complex algorithm with many blocks, but for the purposes ofthis discussion we are only interested with the lossy (ornon-invertible) portion of the algorithm. At the encoder this involves:

Transformation to the YcrCb (or similar space)

DCT (Discrete Cosine Transform) transformation

Quantization of DCT coefficients with a given Q-table and Q-factor

At the decoder this involves:

Inverse quantization with a given Q-table and Q-factor.

Inverse DCT transformation

Inverse Color transformation to RGB.

The loss occurs in the quantization of the DCT coefficients. Eachcoefficient is quantized with a uniform quantizer the stepsize of whichis determined by the appropriate entry in the predefined Q-table, andthe Q-factor. Thus the quantized DCT coefficient is always an integernumber of times the corresponding stepsize.

Observe that there would be no loss if all of the DCT coefficientshappened to be equal to reconstruction levels of the quantizers. This isso because the quantizer represents ranges of possible coefficientvalues by a single reconstruction level. Observe that an image that hasalready been JPEG compressed identically has the property, that if it iscompressed a second time (using the same quantization levels) the imagewill be unchanged. This property is exploited by a modified JPEGcompression approach suitable for producing compressed images for thepost-processing approach herein. This approach is treated in detail inco-pending patent application Ser. No. 08/878,170 (now U.S. Pat. No.5,838,818), filed on even date herewith, Entitled "Artifact ReductionCompression Method and Apparatus for Mosaiced Images", with inventorCormac Herley. Briefly stated, a process and apparatus is describedtherein to improve the fidelity of compressed demosaiced images bydecreasing the error introduced for a given compression ratio. Because(typically) two out of three of the color values at any location of thedemosaiced image are interpolated, most of the loss can be concentratedinto these values, so that the actual or measured data values havelittle loss. This is achieved by finding an interpolation of the datasuch that the original measured values suffer minimal loss in the lossycompression, while the loss for the other interpolated values may bearbitrarily large. Thus, rather than performing an interpolation firstand accepting whatever loss the compression scheme (e.g., JPEG) gives,the values to be interpolated are treated as "Don't cares" and thenprovided so as to minimize the loss for the measured values.

For one embodiment of the color interpolation process, the raw data isthe plane R. We add the two interpolated planes I₀ and I₁ to form a24-bit image. After compression the error is (R-R', I₀ -I₀ ', I₁ -I₁ ').The first component, R-R', is iteratively forced to be small becausethis represents the error at the data locations. This is achieved byreplacing R' with R then compressing and decompressing the resultingimage. This process is repeated until R-R' is sufficiently small, oruntil a predetermined number of iterations have occurred.

Returning to the post-processing scheme, as we have discussed earlier,the images acquired by a digital camera are generally mosaiced. To getthe maximum benefit from the JPEG algorithm it is first necessary totransform to some linear luminance/chrominance space such as YUV orYCrCb. To carry out this transformation it is first necessary todemosaic or color interpolate the image to have a full 24-bit image, orto have its R, G and B values at each of the locations. There are avariety of algorithms that carry out this color interpolation, see forexample, Programmer's Reference Manual Models: DCS200ci, DCS200mi,DCS200c, DCS200m, Eastman Kodak Company, December 1992. For algorithmsthat are to be implemented on a camera, the scheme is usually verysimple, such as bilinear interpolation, or a variation. This falls intothe framework that we have outlined, because the set of images that arecolor interpolated using bilinear interpolation corresponds to a space.The JPEG standard for lossy image compression is also a transform codingmethod, with scalar quantization of the transform coefficients. It thusfits into our framework also. Thus we can use the projection algorithmto improve the estimate of the original image when we deal with a colorinterpolated image that has been JPEG compressed.

Prior Art on this Subject

It is worth pointing out that iterative algorithms have previously beenapplied to restoration of images in general and the reduction of codingartifacts in particular. An example of the former can be found in D. CYoula and H. Webb, Image Restoration by the Method of ConvexProjections: Part I-Theory, IEEE Trans. Med. Imaging, MI-12:81-94,October 1982. Examples of the latter can be found in: S. J. Reeves andS. L. Eddins, Comments on "Iterative Procedures for Reduction ofBlocking Effects in Transform Image Coding", IEEE Trans. Circuits andSystems for Video Technology, 3(6), December 1993; R. Rosenholtz and A.Zakhor, "Iterative Procedures for Reduction of Blocking Effects inTransform Image Coding"; IEEE Trans. Circuits and Systems for VideoTechnology, 2(1):91-95, March 1992; G. Sapiro, "Color SpaceReconstruction of Compressed Images for Digital Photos", PatentDisclosure, Dec. 1994; and Y. Yang, N. P. Galatsanos, and A. K.Katsaggelos, "Regularized Reconstruction to Reduce Blocking Artifacts ofBlock Discrete Cosine Transform Compressed Images", IEEE Trans. Ciruitsand Systems for Video Technology, 3:421-432, December 1993.

As mentioned before, a particular use of an iterative scheme to reduceartifacts introduced by JPEG is described in R. Eschbach, Decompressionof Standard ADCT-compressed Images, U.S. Pat. No. 5,379,122, January1995. The approach there has elements in common with our approach.However, although we constrain (in step 1) the image to belong to therange of images produced by a particular interpolation scheme, theapproach in Eschbach merely involves filtering for high-frequency noise.Because our constraint is well defined (e.g., we know the exact natureof the color interpolation block), we can do a much better job ofimproving the final image than is the case with the Eschbach algorithmwhere the constraint is harder to define.

Further, Step 1 of our algorithm involves an orthogonal projection,which can be implemented with two linear filtering operations and amultirate sampling change. Thus our approach is clearly distinct fromthe method of Eschbach.

FIG. 5 is a flow chart illustrating an interpolated image decompressionprocess 500 that practices image compression artifact reduction aspracticed according to one embodiment of the present invention. In FIG.5, compressed interpolated image 520 is decompressed (510). The closestimage interpolated in a prescribed way is found (530). The closest imagethat compresses to the same compressed output as the original is alsofound (540). A test is then performed (550) to determine whether theclosest interpolated image (found in 530) is close enough to the closestimage that compresses to the same compressed output as the original(found in 540). If the error from compression noise is unacceptable,then steps 530 and 540 are repeated and the resulting images are againcompared (550).

This iterative process is repeated until it is determined (550) thatcompression noise has reduced to an acceptable level or no furtherimprovement is achieved, at which time the final decompressed image(560) is output.

FIG. 6 is a block diagram illustrating an interpolated imagedecompression apparatus 600 that practices image compression artifactreduction as practiced according to one embodiment of the presentinvention. Compressed interpolated input image 610 is uncompressed bydecompressor 620. The uncompressed image is stored in uncompressed imagestore 630. The uncompressed image is provided to interpolation projector640 which finds the closest image interpolated in the prescribed way.The closest interpolated image found by interpolation projector 650 isstored in interpolated image store 650. Similarly, compression projector660 finds the closest image that compresses to the same compressedoutput as the original.

Comparer 670 compares the interpolated image from interpolationprojector 640 to the image from compression projector 660. If the twoimages are not close enough to each other, then the interpolation (640)and compression (670) projections are repeated. Again, the resultingimages are compared (660).

This process iterates until comparer 670 determines that the imagestored in interpolated image store 650 is close enough to the image fromcompression projector 660. When the two images are close enough or nofurther improvement is achieved, comparer 670 causes interpolated imagestore 650 to release the interpolated image stored in interpolated imagestore 620 as uncompressed output image 680. Alternately, rather thanrequiring convergence of the images, the iterations can stop after acertain number of iterations have occurred.

Experimental Results

FIG. 7A is a representative comparison of Root Mean Squared Error of thegreen channel of a bilinear interpolated image as a function ofcompression ratio between a decompression scheme according to oneembodiment of the present invention and a traditional imagedecompression scheme. FIGS. 7B and 7C are corresponding comparisons ofRoot Mean Squared Error of the respective red and blue channels.

In order to test the efficacy of the algorithm, we carried out thepost-processing on bilinearly color interpolated images obtained from aKodak DCS-200 digital camera. We compressed the color image at variouscompression ratios, and compared root mean square error on each of thecolor channels before and after the post-processing. The results areshown in FIGS. 7A-C for the case of a detail of a representative image.In each figure, the upper line is the before post-processing case andthe lower line is the after post-processing case. As can be seen fromthe plots, a very consistent and substantial improvement is obtained ineach of the color channels at all compression ratios.

A particularly appealing aspect of the algorithm is that, whileiterative in nature, a large part of the improvement is realized in thefirst few iterations, and even a single iteration improves the noiseconsiderably.

From a qualitative point of view, we have compared details from imagesbefore and after post-processing. Typically, we have found thepost-processed image to be sharper and to have fewer color aliasingproblems than it posessed before post-processing.

The many features and advantages of the invention are apparent from thewritten description and thus it is intended by the appended claims tocover all such features and advantages of the invention. Further,because numerous modifications and changes will readily occur to thoseskilled in the art, it is not desired to limit the invention to theexact construction and operation as illustrated and described. Hence,all suitable modifications and equivalents may be resorted to as fallingwithin the scope of the invention.

What is claimed is:
 1. A decompression process for a compressedinterpolated image wherein the compressed interpolated image wasinterpolated using a prescribed interpolation method prior tocompressing using a known lossy compression scheme, the processcomprising the steps of:a) finding a first image, the first image beingan image that has been interpolated in the prescribed way; b) finding asecond image, the second image being the interpolated compressed firstimage that has been compressed to the compressed interpolated imageoutput by the compression scheme; and c) if the first image issufficiently different from the second image, repeating steps a) and b).2. The process as set forth in 1, comprising the step of stopping afterperforming step b) a predetermined number of times.
 3. The process asset forth in claim 1, wherein step a) involves performing an orthogonalprojection on a space of interpolated images to find the first image. 4.The process as set forth in claim 3, wherein the interpolated images areinterpolated during a demosaicing process.
 5. The process as set forthin claim 3, wherein the interpolated images are bilinearly interpolated.6. The process as set forth in claim 1, wherein step b) involves findingthe second image by performing an orthogonal projection on the set ofinterpolated images that have been compressed to the compressedinterpolated image.
 7. The process as set forth in claim 6, wherein thecompressed interpolated images are compressed using a discrete cosinetransform scheme.
 8. A decompression processor for a compressedinterpolated image wherein the compressed interpolated image wasinterpolated using a prescribed interpolation method prior tocompressing using a known lossy compression scheme, the processorcomprising:a first projector to find a first image, the first imagebeing an image that has been interpolated in the prescribed way; asecond projector to find a second image, the second image being theinterpolated first image that has been compressed to the compressedinterpolated image output by the compression scheme; and a comparer tocompare the first and second images, and if the first image issufficiently different from the second image, to cause the firstprojector to find a new first image and the second projector to find anew second image.
 9. The processor as set forth in 8, wherein thedecompression process stops after a predetermined number of loops. 10.The processor as set forth in claim 8, wherein the first projectorperforms an orthogonal projection on a space of interpolated images tofind the first image.
 11. The processor as set forth in claim 10,wherein the interpolated images are interpolated during a demosaicingprocess.
 12. The processor as set forth in claim 10, wherein theinterpolated images are bilinearly interpolated.
 13. The processor asset forth in claim 8, wherein the second projection means finds thesecond image by performing an orthogonal projection on the set ofinterpolated images that have been compressed to the compressedinterpolated image.
 14. The processor as set forth in claim 8, whereinthe compressed interpolated images are compressed using a discretecosine transform scheme.
 15. A decompression processor for a compressedinterpolated image wherein the compressed interpolated image wasinterpolated using a prescribed interpolation method prior tocompressing using a known lossy compression scheme, the processorcomprising:first projection means for finding a first image, the firstimage being an image that has been interpolated in the prescribed way;second projection means for finding a second image, the second imagebeing the interpolated first image that has been compressed to thecompressed interpolated image output by the compression scheme; andcomparer means for comparing the first and second images, and if thefirst image is sufficiently different from the second image, for causingthe first projection means to find a new first image and the secondprojection means to find a new second image.